Question

Which side lengths form a right triangle?

Answer 1

B. 1,8,(65)½

Explanation:

For the side lengths to form a right triangle they have to obey the Phythagorean Theorem which when paraphrased says " the square of the longer side is equal to the sum of the squares of the other sides"

A . 2² + 15² = 4 + 225 = 229

17² = 289

Not a Phythagorean triple

B. 1² + 8² = 1 + 64 = 65

(65½)² = 65

A Phythagorean triple

C. 2² + (80½)² = 4 + 80 = 84

9² = 81

Not a Phythagorean triple.

Answer 2

B) 1, 8, √65

Explanation:

For 3 side lengths to form a triangle the sum of two random sides must be bigger than the third side and their differences must be smaller than the third side.

1+8 > √65 because √65 is approximately 8.1

8-1 < √65